Null geodesics and shadow of hairy black holes in Einstein-Maxwell-dilaton gravity

The timelike and null-like geodesics around compact objects are some of the best tools to classify and understand the structure of a space-time. We study the null geodesics around charged static dilaton black holes in Einstein-Maxwell-dilaton gravity. The physical parameters for nonradial geodesics, including the effective potential, effective force, radius of the photon sphere, and impact parameter, are obtained, and effects of the charge parameter and dilaton coupling constant on these quantities are studied. Possible photon motions for different values of the impact parameter are analyzed, and unstable circular orbits and unbounded orbits are plotted. These results are compared to that of Schwarzschild, Reissner-Nordstr\"om, and Gibbons-Maeda-Garfinkle-Horowitz-Strominger black holes. Also, we study the shadow cast by a dilaton black hole and investigate how the dilaton coupling affects the size of the black hole shadow. Finally, as an application of null geodesics, we calculate the deflection of light and investigate the effects of the model parameters on the bending angle.

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